Unemployment
Determining the Natural Rate of Unemployment
Learning Objectives
• To learn that unemployment is the natural consequence of labor force dynamics.
• To understand that the natural rate of unemployment is determined in part by the costs of employment turnover.
• To learn the differences between the various types of unemployment and the policy consequences of each.
Unemployment• The unemployment rate is the number of
unemployed people, expressed as a percentage of the labor force.– Labor Force = (Civilian non-institutional population
over age 16 - People not in the labor force (students, homemakers, retirees, discouraged workers)
– Unemployed = Labor force - People who are employed.
– Unemployment rate = People who are unemployed/Labor force times 100
Natural Rate of Unemployment
• The natural rate of unemployment is the percentage of the labor force that can normally be expected to be unemployed for reasons other than cyclical fluctuations in real GDP.– The natural rate of unemployment is related to
the willingness of workers to voluntarily separate from their jobs, job loss, the duration of unemployment periods, the rate of change in the pattern of demand, and changes in technology.
What Causes Unemployment?
• Frictional Unemployment– Job Search
• It takes time to match workers and jobs.
• Structural Unemployment– Skill Mismatch
• Unemployed workers’ skills do not match the needs of employers.
– Location Mismatch• Unemployed workers’ location do not match the location of
the jobs.
What Causes Unemployment?
• Cyclical Unemployment– Real-Wage Rigidity
• The failure of wages to adjust, either rising or falling, until labor supply equals labor demand.
• Real wage rigidity can be caused by minimum wage laws, unions and collective bargaining, and efficiency wages.
New-Keynesian Theory of Unemployment
• Assumptions:– The firm recognizes that its pool of workers is a
stock and that any given stock can be associated with fast or slow labor turnover.
– The firm minimizes the costs of maintaining a stock of employees by adjusting the real wage.
– The firm demands fewer workers as the real wage rises, so employment is a decreasing function of the real wage.
New-Keynesian Theory of Unemployment
• Assumptions:– The stock of workers sent to the labor market
by households is the “labor force.”• Households supply more workers when the real
wage rises, so the labor force is an increasing function of the real wage.
New-Keynesian Theory of Unemployment
• The new-Keynesian theory differs from the classical theory in that the wage does not equate labor demand and labor supply.
• Rather, the wage is set at a point where there is still a pool of unemployed workers.
• This wage is called the efficiency wage and the level of unemployment associated with it is called the natural rate of unemployment.
Flows Through the Labor Market
The supply of labor is a flowinto the labor market.
The demand for labor is a flowout of the labor market.
Stock of Unemployed
Unemployment is the stock of workers who are not matched with firms.
Macroeconomics, Roger Farmer, p. 177
Efficiency Wage Theories
• High wages make workers more productive or efficient.– Firms are reluctant to cut wages despite an
excess supply of labor because it would lower worker productivity.
• Higher wages reduce labor turnover.
• Average quality of a firm’s workforce depends on the wages paid.
• High wages improve worker effort.
w/P
0E(w/P)
LF
(w/P)*
NRU
The labor force (LF) is an increasing function of the real wage.
Employment, E(w/P), is a decreasing function of the real wage.
The efficiency wage does not occur at the intersection of E(w/P) and LF.
When the real wage equals the efficiency wage, unemployment is at its natural rate.
E* LF*
Employment and Labor Force
New-Keynesian Theory of Unemployment
Turnover Cost and the Efficiency Wage Model
• Assumptions:– Firms must search for workers actively, but
they may vary the intensity of their search.– Firms choose the wages they offer to minimize
their wage bills, which are comprised of turnover costs and the real wage.
• One element of the wage bill is the real wage (w/P); the other element is the cost of recruiting new workers, C(w/P, L).
Turnover Cost and the Efficiency Wage Model
• Assumptions:– Turnover cost = C(w/P, L) = c(w/P)L
• Turnover cost, C, is a function of the real wage and employment.– The firm can influence C by offering a different real wage and/or by
changing the number of workers it employs.
• C is inversely related to the real wage.– Better-paid workers are more likely to remain with the firm; thereby,
lowering the firm’s turnover costs.
• The marginal benefit of an increase in the real wage equals the reduction in turnover cost for a given increase in the real wage.
• The marginal benefit decreases as the real wage increases.
Turnover Cost and the Efficiency Wage Model
• Assumptions continued:– Per worker turnover cost = c(w/P)L
• Turnover costs are proportional to the number of workers.
Choosing the Efficiency Wage
• Each firm chooses its wage rate to minimize the cost of maintaining a pool of employed workers.
• The firm’s profit function is: = Y – w/P(L) – c(w/P)L where
= Profit
Y = Commodities supplied
w/P(L) = Cost of labor demanded
c(w/P)L = Turnover cost per worker
Choosing the Efficiency Wage
• Process for Choosing the Efficiency Wage1. The firm minimizes costs per worker by choosing the efficiency wage that makes w/P + c(w/P) as small as possible.
2. Given the efficiency wage, the firm chooses its level of employment (L) to maximize profit.
Choosing the Efficiency Wage
• If the wage increases by one dollar, the firm’s wage bill increases by one dollar per worker.– This is the marginal cost of a change in the
wage.
• If the wage increases by one dollar, the firm’s turnover cost decreases.– This is the marginal benefit of a change in the
wage.
Choosing the Efficiency Wage
MB=c(w/P)
MC
MBMC
0 w/Pw/P*
The efficiency wage equates the marginal benefit of increasing the real wage to its marginal cost.
Deriving the Efficiency Wage: Math
• c = 1 – 2(w/P) + (w/P)2
– Turnover cost depends on the real wage.• Note that as w/P increases, turnover cost falls*
• dc/(w/P) = – (– 2 + 2(w/P)) – The marginal benefit is the slope of the cost function.
• We use the negative because the negative of a cost is a benefit.
• Note that the marginal benefit falls as the real wage rises.
• Marginal cost = 1.
*Where w/P is assumed to be <1, and if (w/P) >1, c = 0
Deriving the Efficiency Wage: Math
• Costs are minimized at the real wage where marginal benefit equals marginal cost.– Marginal benefit = – (– 2 + 2(w/P)) – Marginal cost = 1.
1 = 2 –2(w/P)
(1 – 2)/ – 2 = w/P
½ = w/P
Choosing a Stock of Workers
• The firm pays a real wage and a turnover cost for each worker.– The additional cost means that at every real
wage the firm hires fewer workers than would be predicted in the classical model.
Choosing a Stock of Workers
0
w/P
E
LDC
EW
LDC represents the classical labor
wage to the marginal product of labor.
EW represents the efficiencywage employment curve. Itequates the real wage to the marginal product of labor minusthe turnover cost.
Choosing a Stock of Workers
0
w/P
w/P
E
LDC
EW
E* EC
The gap between LDC and EW
is turnover cost. It is smaller whenthe real wage is higher because fora high real wage, the turnover cost is lower.
EC represents employment in the classical model.
E* represents employment in theefficiency wage model.
Deriving the Labor Demand Curve: Math
= LD – (1/2)(LD)2 – (w/P)LD – c(w/P)LD
• where• Profit =
• The production function = LD – (1/2)(LD)2
• The wage bill = (w/P)LD
• Turnover cost = c(w/P)LD
Deriving the Labor Demand Curve: Math
• c = 1 – 2(w/P) + (w/P)2
w/P = ½ so c = ¼
• Marginal product = 1 – LD
• To maximize profit, the firm equates marginal product to the real wage plus turnover cost.
1 – LD = (w/P) + c(w/P) = ½ + ¼ = ¾ LD = 1 – ¾ = ¼
w/P
0E(w/P)
LF
(w/P)*
NRUAt equilibrium, the efficiency wage, (w/P)*, is chosen to maximize profits.
When the real wage equals the efficiency wage, the natural rate of unemployment is the difference between the labor force and the quantity of employment.
E* LF*
Employment and Labor Force
New-Keynesian Theory of Unemployment
Deriving the Natural Rate of Unemployment: Math
• LS = w/P = ½– where
• LS = labor supply
• w/P = the real wage
• The natural rate of unemployment, U*, is given by the difference between demand and supply.– U* = ½ – ¼ = ¼
